On the Correctness of Rough-Set Based Approximate Reasoning
There is a natural generalization of an indiscernibility relation used in rough set theory, where rather than partitioning the universe of discourse into indiscernibility classes, one can consider a covering of the universe by similarity-based neighborhoods with lower and upper approximations of relations defined via the neighborhoods. When taking this step, there is a need to tune approximate reasoning to the desired accuracy. We provide a framework for analyzing self-adaptive knowledge structures. We focus on studying the interaction between inputs and output concepts in approximate reasoning. The problems we address are:
given similarity relations modeling approximate concepts, what are similarity relations for the output concepts that guarantee correctness of reasoning?
assuming that output similarity relations lead to concepts which are not accurate enough, how can one tune input similarities?
Unable to display preview. Download preview PDF.
- 3.Doherty, P., Kachniarz, J., Szałas, A.: Using contextually closed queries for local closed-world reasoning in rough knowledge databases. In: Pal, et al Google Scholar
- 4.Doherty, P., Łukaszewicz, W., Skowron, A., Szałas, A.: Approximation transducers and trees: A technique for combining rough and crisp knowledge. In: Pal, et al Google Scholar
- 9.Doherty, P., Szałas, A.: On the correspondence between approximations and similarity. In: Tsumoto, S., Slowinski, R., Komorowski, J., Grzymala-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 143–152. Springer, Heidelberg (2004)Google Scholar
- 10.Gabbay, D.M., Schmidt, R., Szałas, A.: Second-Order Quantifier Elimination. In: Foundations, Computational Aspects and Applications. Studies in Logic, vol. 12. College Publications (2008)Google Scholar
- 12.Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neuro Computing: Techniques for Computing with Words. Springer, Heidelberg (2003)Google Scholar
- 15.Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P. (ed.) Advances in Machine Intelligence & Soft Computing, Raleigh, NC, pp. 17–33. Bookwrights (1997)Google Scholar